1971 AHSME Problem 24

Pascal's triangle is an array of positive integers(See figure), in which the first row is 1, the second row is two 1's, each row begins and ends with 1, and the k^\text{th} number in any row when it is not 1, is the sum of the k^\text{th} and (k-1)^\text{th} numbers in the immediately preceding row. The quotient of the number of numbers in the first n rows which are not 1's and the number of 1's is

\textbf{(A) }\dfrac{n^2-n}{2n-1}\qquad \textbf{(B) }\dfrac{n^2-n}{4n-2}\qquad \textbf{(C) }\dfrac{n^2-2n}{2n-1}\qquad \textbf{(D) }\frac{n^2-3n+2}{4n-2}\qquad \textbf{(E) }\text{None of these}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.